# Full text of "Treatise On Analysis Vol-Ii"

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```452       INDEX

Seminorm: 12.14

Separation (of two sets by a hyperplane):

12.15, prob. 4

Series in a topological vector space: 12.14
Simple convergence, limit: 12.5
Simple normal operator: 15.11
Simplex: 14.3
Spectral value of an element of a normed

algebra: 15.2
Spectrum of an element of a Banach algebra:

15.2

Spectrum of a Banach algebra: 15.3
Spectrum of an unbounded operator: 15.12
Square-mtegrable function: 13.11
Stabilizer of a point: 12.10
Stable subspace (for a representation): 15.5
Star algebra: 15.4

Steiner symmetrization: 14.3, prob. 8
Stem's theorem: 14.10, prob. 4
Step function: 13.9
Stieltjes measure: 13.8, prob. 6
Stieltjes' moment problem: 13.20, prob. 5
Stieltjes transform: 14.11, prob. 16
Strict morphism: 12.12
Strong topology: 12.15
Subspace: 12.2

Sum of a series with positive terms: 13.5
Support of a function: 12.6
Support of a measure: 13.19
Symmetric neighborhood: 12.8
Szego-Kolmogoroff-Krein theorem: 15.3,

prob.11

Tessellation (G-): 14.1, prob. 6
Thue's theorem: 14.2, prob. 2
Titchmarsh-Kodaira formula: 15.12, prob.

9

Topological group: 12.8
Topological isomorphism of normed (or

normable) algebras: 15.1
Topological space: 12.1
Topological zero-divisor: 15.2, prob. 3
Topologically cyclic representation: 15.5

Topologically equivalent families of pseudo-
distances: 12.4

Topologically irreducible representation:
15.5

Topologically nilpotent: 15.2, prob. 5

Topologically simple: 15.8

Topology: 12.1

Topology defined by a distance: 12.1

Topology defined by a family of pseudo-
distances: 12.4

Topology defined by a family of seminorms:
12.14

Topology of convergence in measure: 13.12,
prob. 2

Topology of simple convergence: 12.15

Torus: 14.2

Total mass of a bounded measure: 13.9

Totalizer: 15.5

Trace of an operator: 15.11, prob. 7

Transitively (group acting): 12.10

Translation of a function or measure: 14.1

Transpose of a continuous linear mapping:
12.15

Trivial action: 12.10

Type (p,q) (operator): 13.17, prob. 7

U

Unbounded operator: 15.12

Uniformizable space: 12.4

Unimodular group; 14.3

Unitary element: 15.4

Unitary group: 12.15, prob. 8

Universally measurable: 13.9

Upper envelope of a family of real-valued

functions: 12.7
Upper integral: 13.5
Upper semicontinuous function: 12.7

Vague topology: 13.4

Vaguely bounded, convergent, continuous:

13.4
von  Neumann's  ergodic theorem: 12.15,

prob.12
von Neumann's theorem on unbounded

normal operators: 15.12entiable:
```